Constant velocity universal joints interconnect driving and driven shafts in a manner that permits relative angular movement between the rotational axes of the shafts while still providing constant angular velocity of the driven shaft at the same rate as the driving shaft throughout each revolution. Inner and outer races of such joints are respectively connected to the shafts and each race has pairs of diametrically opposite grooves which are spaced circumferentially and receive ball elements for interconnecting the races. Each groove defines a partially circular arc and has a partially circular or arch cross section of less than 180.degree. so as to receive one side of the associated ball element whose other side is received within an aligned groove in the other race. Grooves in the inner race face outwardly toward the outer race, while the grooves in the outer race face inwardly toward the inner race which is received within the outer race. During angular movement between the rotational axes of the driving and driven shafts connected to the races, forces applied to the ball elements by a cage provide movement of the ball elements along the grooves in order to maintain the ball elements in a plane which bisects the angle between the rotational axes. As such, the rotational speed of the driven shaft is always the same as that of the driving shaft throughout each revolution. Each race groove and ball element must be ground to a relative precise tolerance, on the order of about one to several ten thousandths of an inch, in order to maintain the ball element positioning that results in the constant speed driving and so that the ball elements uniformly share the torque load without overloading one or a few of the ball elements.
Conventional grinding machines for grinding the inner races of constant velocity universal joints include a rotatable grinding wheel and a rotatable race holder whose axes of rotation are parallel to each other. Movement of the rotating grinding wheel toward the rotating holder with a race held thereon engages the wheel with a pair of diametrically opposite grooves in the race to perform grinding of one pair of grooves at a time. After one pair of grooves is ground, the grinding wheel is moved away from the holder and the holder rotation is then momentarily stopped to permit rotational indexing of the race. Thereafter, the holder is again rotated to grind the next pair of diametrically opposite grooves. Production output of such grinding machines is limited by the necessity of stopping and then starting the holder rotation for the indexing prior to grinding each pair of grooves, and this limited output is necessarily reflected in the cost of the constant velocity universal joint with which the ground inner race is incorporated.